Solution Manual for Precalculus, 11th Edition

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SOLUTIONS MANUAL
TIM BRITT
Jackson State Community College
P RECALCULUS
ELEVENTH EDITION
Michael Sullivan
Chicago State University

Table of Contents
Chapter 1 Graphs
1.1 The Distance and Midpoint Formulas ......................................................................................... 1
1.2 Graphs of Equations in Two Variables; Intercepts; Symmetry ................................................ 13
1.3 Lines ......................................................................................................................................... 26
1.4 Circles ....................................................................................................................................... 43
Chapter Review................................................................................................................................ 56
Chapter Test ..................................................................................................................................... 62
Chapter Projects ............................................................................................................................... 64
Chapter 2 Functions and Their Graphs
2.1 Functions................................................................................................................................... 65
2.2 The Graph of a Function ........................................................................................................... 83
2.3 Properties of Functions ............................................................................................................. 92
2.4 Library of Functions; Piecewise-defined Functions ............................................................... 109
2.5 Graphing Techniques: Transformations ................................................................................. 121
2.6 Mathematical Models: Building Functions ............................................................................. 139
Chapter Review.............................................................................................................................. 147
Chapter Test ................................................................................................................................... 154
Cumulative Review ....................................................................................................................... 157
Chapter Projects ............................................................................................................................. 161
Chapter 3 Linear and Quadratic Functions
3.1 Properties of Linear Functions and Linear Models ................................................................. 163
3.2 Building Linear Functions from Data ..................................................................................... 174
3.3 Quadratic Functions and Their Properties .............................................................................. 180
3.4 Build Quadratic Models from Verbal Descriptions and from Data ........................................ 203
3.5 Inequalities Involving Quadratic Functions ............................................................................ 211
Chapter Review.............................................................................................................................. 231
Chapter Test ................................................................................................................................... 239
Cumulative Review........................................................................................................................ 241
Chapter Projects ............................................................................................................................. 244
Chapter 4 Polynomial and Rational Functions
4.1 Polynomial Functions ............................................................................................................. 247
4.2 Graphing Polynomial Functions; Models ............................................................................... 257
4.3 Properties of Rational Functions............................................................................................. 273
4.4 The Graph of a Rational Function .......................................................................................... 283
4.5 Polynomial and Rational Inequalities ..................................................................................... 339
4.6 The Real Zeros of a Polynomial Function .............................................................................. 360
4.7 Complex Zeros; Fundamental Theorem of Algebra ............................................................... 391
Chapter Review.............................................................................................................................. 400
Chapter Test ................................................................................................................................... 415
Cumulative Review........................................................................................................................ 419
Chapter Projects ............................................................................................................................. 424

Chapter 5 Exponential and Logarithmic Functions
5.1 Composite Functions .............................................................................................................. 426
5.2 One-to-One Functions; Inverse Functions .............................................................................. 444
5.3 Exponential Functions ............................................................................................................ 466
5.4 Logarithmic Functions ............................................................................................................ 487
5.5 Properties of Logarithms ........................................................................................................ 509
5.6 Logarithmic and Exponential Equations ................................................................................. 518
5.7 Financial Models .................................................................................................................... 538
5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models .................................................................................................................... 546
5.9 Building Exponential, Logarithmic, and Logistic Models from Data..................................... 555
Chapter Review.............................................................................................................................. 561
Chapter Test ................................................................................................................................... 573
Cumulative Review........................................................................................................................ 577
Chapter Projects ............................................................................................................................. 580
Chapter 6 Trigonometric Functions
6.1 Angles, Arc Length, and Circular Motion .............................................................................. 583
6.2 Trigonometric Functions: Unit Circle Approach .................................................................... 592
6.3 Properties of the Trigonometric Functions ............................................................................. 610
6.4 Graphs of the Sine and Cosine Functions ............................................................................... 624
6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions...................................... 645
6.6 Phase Shift; Sinusoidal Curve Fitting ..................................................................................... 655
Chapter Review.............................................................................................................................. 666
Chapter Test ................................................................................................................................... 674
Cumulative Review........................................................................................................................ 678
Chapter Projects ............................................................................................................................. 682
Chapter 7 Analytic Trigonometry
7.1 The Inverse Sine, Cosine, and Tangent Functions .................................................................. 685
7.2 The Inverse Trigonometric Functions (Continued) ................................................................ 698
7.3 Trigonometric Equations ........................................................................................................ 710
7.4 Trigonometric Identities ......................................................................................................... 731
7.5 Sum and Difference Formulas ................................................................................................ 744
7.6 Double-angle and Half-angle Formulas .................................................................................. 769
7.7 Product-to-Sum and Sum-to-Product Formulas...................................................................... 795
Chapter Review.............................................................................................................................. 808
Chapter Test ................................................................................................................................... 823
Cumulative Review........................................................................................................................ 828
Chapter Projects ............................................................................................................................. 834
Chapter 8 Applications of Trigonometric Functions
8.1 Right Triangle Trigonometry; Applications ........................................................................... 838
8.2 The Law of Sines .................................................................................................................... 852
8.3 The Law of Cosines ................................................................................................................ 867
8.4 Area of a Triangle ................................................................................................................... 879
8.5 Simple Harmonic Motion; Damped Motion; Combining Waves ........................................... 889
Chapter Review.............................................................................................................................. 899
Chapter Test ................................................................................................................................... 905
Cumulative Review........................................................................................................................ 909
Chapter Projects ............................................................................................................................. 915

Chapter 9 Polar Coordinates; Vectors
9.1 Polar Coordinates.................................................................................................................... 919
9.2 Polar Equations and Graphs .................................................................................................... 928
9.3 The Complex Plane; De Moivre’s Theorem ........................................................................... 958
9.4 Vectors .................................................................................................................................... 971
9.5 The Dot Product ...................................................................................................................... 984
9.6 Vectors in Space ..................................................................................................................... 990
9.7 The Cross Product................................................................................................................... 996
Chapter Review............................................................................................................................ 1007
Chapter Test ................................................................................................................................. 1016
Cumulative Review...................................................................................................................... 1020
Chapter Projects ........................................................................................................................... 1023
Chapter 10 Analytic Geometry
10.2 The Parabola ....................................................................................................................... 1026
10.3 The Ellipse .......................................................................................................................... 1041
10.4 The Hyperbola .................................................................................................................... 1058
10.5 Rotation of Axes; General Form of a Conic ....................................................................... 1078
10.6 Polar Equations of Conics ................................................................................................... 1091
10.7 Plane Curves and Parametric Equations ............................................................................. 1100
Chapter Review............................................................................................................................ 1115
Chapter Test ................................................................................................................................. 1124
Cumulative Review...................................................................................................................... 1129
Chapter Projects ........................................................................................................................... 1131
Chapter 11 Systems of Equations and Inequalities
11.1 Systems of Linear Equations: Substitution and Elimination ............................................... 1135
11.2 Systems of Linear Equations: Matrices .............................................................................. 1158
11.3 Systems of Linear Equations: Determinants ....................................................................... 1183
11.4 Matrix Algebra .................................................................................................................... 1197
11.5 Partial Fraction Decomposition .......................................................................................... 1216
11.6 Systems of Nonlinear Equations ......................................................................................... 1235
11.7 Systems of Inequalities ....................................................................................................... 1263
11.8 Linear Programming ........................................................................................................... 1279
Chapter Review............................................................................................................................ 1292
Chapter Test ................................................................................................................................. 1307
Cumulative Review...................................................................................................................... 1316
Chapter Projects ........................................................................................................................... 1319
Chapter 12 Sequences; Induction; the Binomial Theorem
12.1 Sequences............................................................................................................................ 1322
12.2 Arithmetic Sequences ......................................................................................................... 1332
12.3 Geometric Sequences; Geometric Series ............................................................................ 1341
12.4 Mathematical Induction ...................................................................................................... 1353
12.5 The Binomial Theorem ....................................................................................................... 1362
Chapter Review............................................................................................................................ 1369
Chapter Test ................................................................................................................................. 1373
Cumulative Review...................................................................................................................... 1376
Chapter Projects ........................................................................................................................... 1379

Chapter 13 Counting and Probability
13.1 Counting.............................................................................................................................. 1382
13.2 Permutations and Combinations ......................................................................................... 1385
13.3 Probability ........................................................................................................................... 1390
Chapter Review............................................................................................................................ 1397
Chapter Test ................................................................................................................................. 1399
Cumulative Review...................................................................................................................... 1400
Chapter Projects ........................................................................................................................... 1403
Chapter 14 A Preview of Calculus: The Limit, Derivative, and Integral of a Function
14.1 Investigating Limits Using Tables and Graphs ................................................................... 1406
14.2 Algebraic Techniques for Finding Limits ........................................................................... 1412
14.3 One-sided Limits; Continuity.............................................................................................. 1416
14.4 The Tangent Problem; The Derivative................................................................................ 1423
14.5 The Area Problem; The Integral ......................................................................................... 1432
Chapter Review............................................................................................................................ 1446
Chapter Test ................................................................................................................................. 1453
Chapter Projects ........................................................................................................................... 1456
Appendix A Review
A.1 Algebra Essentials ................................................................................................................ 1462
A.2 Geometry Essentials ............................................................................................................. 1467
A.3 Polynomials.......................................................................................................................... 1473
A.4 Synthetic Division ................................................................................................................ 1481
A.5 Rational Expressions ............................................................................................................ 1483
A.6 Solving Equations ................................................................................................................ 1488
A.7 Complex Numbers; Quadratic Equations in the Complex Number System ........................ 1502
A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications ..... 1508
A.9 Interval Notation; Solving Inequalities ................................................................................ 1515
A.10 nth Roots; Rational Exponents ............................................................................................ 1527
Appendix B Graphing Utilities
B.1 The Viewing Rectangle ........................................................................................................ 1537
B.2 Using a Graphing Utility to Graph Equations ...................................................................... 1538
B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry ............................ 1543
B.5 Square Screens ..................................................................................................................... 1545

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1
Chapter 1
Graphs
Section 1.1
1. 0
2.  5 3 8 8   
3. 2 2
3 4 25 5  
4. 2 2 2
11 60 121 3600 3721 61    
Since the sum of the squares of two of the sides
of the triangle equals the square of the third side,
the triangle is a right triangle.
5. 1
2 bh
6. true
7. x-coordinate or abscissa; y-coordinate or
ordinate
8. quadrants
9. midpoint
10. False; the distance between two points is never
negative.
11. False; points that lie in Quadrant IV will have a
positive x-coordinate and a negative y-coordinate.
The point  1, 4 lies in Quadrant II.
12. True; 1 2 1 2
,
2 2
x x y y
M   
  
 
13. b
14. a
15. (a) Quadrant II
(b) x-axis
(c) Quadrant III
(d) Quadrant I
(e) y-axis
(f) Quadrant IV
16. (a) Quadrant I
(b) Quadrant III
(c) Quadrant II
(d) Quadrant I
(e) y-axis
(f) x-axis
17. The points will be on a vertical line that is two
units to the right of the y-axis.

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Chapter 1: Graphs
2
18. The points will be on a horizontal line that is
three units above the x-axis.
19. 2 2
1 2
2 2
( , ) (2 0) (1 0)
2 1 4 1 5
d P P    
    
20. 2 2
1 2
2 2
( , ) ( 2 0) (1 0)
( 2) 1 4 1 5
d P P     
     
21. 2 2
1 2
2 2
( , ) ( 2 1) (2 1)
( 3) 1 9 1 10
d P P     
     
22.  2 2
1 2
2 2
( , ) 2 ( 1) (2 1)
3 1 9 1 10
d P P     
    
23.   
 
22
1 2
22
( , ) (5 3) 4 4
2 8 4 64 68 2 17
d P P     
     
24.     
 
2 2
1 2
2 2
( , ) 2 1 4 0
3 4 9 16 25 5
d P P     
     
25.  2 2
1 2
2 2
( , ) 4 ( 7) (0 3)
11 ( 3) 121 9 130
    
     
d P P
26.    2 2
1 2
2 2
( , ) 4 2 2 ( 3)
2 5 4 25 29
d P P     
    
27.  22
1 2
2 2
( , ) (6 5) 1 ( 2)
1 3 1 9 10
    
    
d P P
28.    2 2
1 2
2 2
( , ) 6 ( 4) 2 ( 3)
10 5 100 25
125 5 5
d P P      
   
 
29.    2 2
1 2
2 2
( , ) 2.3 ( 0.2) 1.1 (0.3)
2.5 0.8 6.25 0.64
6.89 2.62
    
   
 
d P P
30.    2 2
1 2
2 2
( , ) 0.3 1.2 1.1 2.3
( 1.5) ( 1.2) 2.25 1.44
3.69 1.92
    
     
 
d P P
31. 2 2
1 2
2 2 2 2
( , ) (0 ) (0 )
( ) ( )
d P P a b
a b a b
   
     
32. 2 2
1 2
2 2
2 2 2
( , ) (0 ) (0 )
( ) ( )
2 2
d P P a a
a a
a a a

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Section 1.1: The Distance and Midpoint Formulas
3
Verifying that ∆ ABC is a right triangle by the
Pythagorean Theorem:
     
     
2 2 2
2 2 2
( , ) ( , ) ( , )
13 13 26
13 13 26
26 26
d A B d B C d A C 
 
 

The area of a triangle is 1
2
A bh  . In this
problem,
   1 ( , ) ( , )
2
1 113 13 13
2 2
13 square units2
A d A B d B C 
   

34. ( 2, 5), (12, 3), (10, 11)A B C    
 
 
 
2 2
2 2
2 2
2 2
2 2
2 2
( , ) 12 ( 2) (3 5)
14 ( 2)
196 4 200
10 2
( , ) 10 12 ( 11 3)
( 2) ( 14)
4 196 200
10 2
( , ) 10 ( 2) ( 11 5)
12 ( 16)
144 256 400
20
d A B
d B C
d A C
    
  
  

    
   
  

     
  
  

Verifying that ∆ ABC is a right triangle by the
Pythagorean Theorem:
     
     
2 2 2
2 2 2
( , ) ( , ) ( , )
10 2 10 2 20
200 200 400
400 400
d A B d B C d A C 
 
 

The area of a triangle is 1
2
A bh . In this
problem,
   
1 ( , ) ( , )
2
1 10 2 10 2
2
1 100 2 100 square units
2
A d A B d B C  
  
   
35. ( 5,3), (6, 0), (5,5)A B C   
 
 
 
2 2
2 2
2 2
2 2
2 2
2 2
( , ) 6 ( 5) (0 3)
11 ( 3) 121 9
130
( , ) 5 6 (5 0)
( 1) 5 1 25
26
( , ) 5 ( 5) (5 3)
10 2 100 4
104
2 26
d A B
d B C
d A C
    
    

   
    

    
   


Verifying that ∆ ABC is a right triangle by the
Pythagorean Theorem:

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Chapter 1: Graphs
4
     
     
2 2 2
2 2 2
( , ) ( , ) ( , )
104 26 130
104 26 130
130 130
d A C d B C d A B 
 
 

The area of a triangle is 1
2
A bh . In this
problem,
   1 ( , ) ( , )
2
1 104 26
2
1 2 26 26
2
1 2 26
2
26 square units
A d A C d B C  
  
  
  

36. ( 6, 3), (3, 5), ( 1, 5)A B C     
 
 
 
2 2
2 2
2 2
2 2
2 2
2 2
( , ) 3 ( 6) ( 5 3)
9 ( 8) 81 64
145
( , ) 1 3 (5 ( 5))
( 4) 10 16 100
116 2 29
( , ) 1 ( 6) (5 3)
5 2 25 4
29
d A B
d B C
d A C
     
    

     
    
 
     
   

Verifying that ∆ ABC is a right triangle by the
Pythagorean Theorem:
     
     
2 2 2
2 2 2
( , ) ( , ) ( , )
29 2 29 145
29 4 29 145
29 116 145
145 145
d A C d B C d A B 
 
  
 

The area of a triangle is 1
2
A bh . In this
problem,
   1 ( , ) ( , )
2
1 29 2 29
2
1 2 29
2
29 square units
A d A C d B C  
  
  

37. (4, 3), (0, 3), (4, 2)A B C    
 
   
 
22
2 2
2 2
2 2
22
2 2
( , ) (0 4) 3 ( 3)
( 4) 0 16 0
16
4
( , ) 4 0 2 ( 3)
4 5 16 25
41
( , ) (4 4) 2 ( 3)
0 5 0 25
25
5
d A B
d B C
d A C
     
    


    
   

    
   


Verifying that ∆ ABC is a right triangle by the
Pythagorean Theorem:

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Section 1.1: The Distance and Midpoint Formulas
5
     
 
2 2 2
2
2 2
( , ) ( , ) ( , )
4 5 41
16 25 41
41 41
d A B d A C d B C 
 
 

The area of a triangle is 1
2
A bh . In this
problem,
   1 ( , ) ( , )
2
1 4 5
2
10 square units
A d A B d A C  
  

38. (4, 3), (4, 1), (2, 1)A B C   
 
   
 
22
2 2
2 2
2 2
22
2 2
( , ) (4 4) 1 ( 3)
0 4
0 16
16
4
( , ) 2 4 1 1
( 2) 0 4 0
4
2
( , ) (2 4) 1 ( 3)
( 2) 4 4 16
20
2 5
d A B
d B C
d A C
    
 
 


   
    


    
    


Verifying that ∆ ABC is a right triangle by the
Pythagorean Theorem:
     
 
2 2 2
2
2 2
( , ) ( , ) ( , )
4 2 2 5
16 4 20
20 20
d A B d B C d A C 
 
 

The area of a triangle is 1
2
A bh . In this problem,
   1 ( , ) ( , )
2
1 4 2
2
4 square units
A d A B d B C  
  

39. The coordinates of the midpoint are:
1 2 1 2
( , ) ,
2 2
4 43 5 ,
2 2
8 0
,
2 2
(4, 0)
x x y y
x y   
  
 
  
  
 
 
  
 

40. The coordinates of the midpoint are:
 
1 2 1 2
( , ) ,
2 2
2 2 0 4
,
2 2
0 4
,
2 2
0, 2
x x y y
x y   
  
 
   
  
 
 
  
 

41. The coordinates of the midpoint are:
1 2 1 2
( , ) ,
2 2
1 8 4 0
,
2 2
7 4
,
2 2
7 , 2
2
  
  
 
   
  
 
 
  
 
 
  
 
x x y y
x y

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Chapter 1: Graphs
6
42. The coordinates of the midpoint are:
1 2 1 2
( , ) ,
2 2
2 4 3 2
,
2 2
6 1
,
2 2
1
3, 2
x x y y
x y   
  
 
   
  
 
 
  
 
 
  
 
43. The coordinates of the midpoint are:
1 2 1 2
( , ) ,
2 2
7 9 5 1
,
2 2
416 ,
2 2
(8, 2)
  
  
 
   
  
 
 
  
 
 
x x y y
x y
44. The coordinates of the midpoint are:
1 2 1 2
( , ) ,
2 2
4 2 3 2
,
2 2
2 1
,
2 2
1
1, 2
x x y y
x y   
  
 
    
  
 
  
  
 
 
   
 
45. The coordinates of the midpoint are:
1 2 1 2
( , ) ,
2 2
0 0
,
2 2
,
2 2
x x y y
x y
a b
a b
  
  
 
  
  
 
 
  
 
46. The coordinates of the midpoint are:
1 2 1 2
( , ) ,
2 2
0 0
,
2 2
,
2 2
x x y y
x y
a a
a a
  
  
 
  
  
 
 
  
 
47. The x coordinate would be 2 3 5  and the y
coordinate would be 5 2 3  . Thus the new
point would be  5,3 .
48. The new x coordinate would be 1 2 3    and
the new y coordinate would be 6 4

Loading page 12...

Section 1.1: The Distance and Midpoint Formulas
7
50. a. If we use a right triangle to solve the
problem, we know the hypotenuse is 17 units in
length. One of the legs of the triangle will be
2+6=8. Thus the other leg will be:
2 2 2
2
2
8 17
64 289
225
15
b
b
b
b
 
 


Thus the coordinates will have an x value of
1 15 14   and 1 15 16  . So the points are
 14, 6  and  16, 6 .
b. Consider points of the form  , 6x  that are
a distance of 17 units from the point  1, 2 .
   
    
 
2 2
2 1 2 1
22
22
2
2
1 2 6
2 1 8
2 1 64
2 65
d x x y y
x
x x
x x
x x
   
    
   
   
  
 
  
2
2
2 2
2
2
17 2 65
17 2 65
289 2 65
0 2 224
0 14 16
x x
x x
x x
x x
x x
  
  
  
  
  
14 0
14
x
x
 
 
or 16 0
16
x
x
 

Thus, the points  14, 6  and  16, 6 are a
distance of 13 units from the point  1, 2 .
51. Points on the x-axis have a y-coordinate of 0. Thus,
we consider points of the form  , 0x that are a
distance of 6 units from the point  4, 3 .
   
   
 
2 2
2 1 2 1
2 2
22
2
2
4 3 0
16 8 3
16 8 9
8 25
d x x y y
x
x x
x x
x x
   
    
    
   
  
 
2
2
2 2
2
2
2
6 8 25
6 8 25
36 8 25
0 8 11
( 8) ( 8) 4(1)( 11)
2(1)
8 64 44 8 108
2 2
8 6 3 4 3 3
2
x x
x x
x x
x x
x
  
  
  
  
     

  
 

  

Loading page 13...

Chapter 1: Graphs
8
 
2
2
2 2
2
2
2
6 6 25
6 6 25
36 6 25
0 6 11
( 6) (6) 4(1)( 11)
2(1)
6 36 44 6 80
2 2
6 4 5 3 2 5
2
y y
y y
y y
y y
y
  
  
  
  
   

    
 
 
   
3 2 5y    or 3 2 5y   
Thus, the points  0, 3 2 5  and  0, 3 2 5 
are on the y-axis and a distance of 6 units from the
point  4, 3 .
53. a. To shift 3 units left and 4 units down, we
subtract 3 from the x-coordinate and subtract
4 from the y-coordinate.
   2 3,5 4 1,1   
b. To shift left 2 units and up 8 units, we
subtract 2 from the x-coordinate and add 8 to
the y-coordinate.
   2 2,5 8 0,13  
54. Let the coordinates of point B be  ,x y . Using
the midpoint formula, we can write
  1 8
2,3 ,
2 2
x y   
  
  .
This leads to two equations we can solve.
1 2
2
1 4
5
x
x
x
  
  

8 3
2
8 6
2
y
y
y
 
 
 
Point B has coordinates  5, 2 .
55.   1 2 1 2
, ,
2 2
x x y y
M x y   
  

Loading page 14...

Section 1.1: The Distance and Midpoint Formulas
9
58. Let 1 2(0, 0), (0, 4), ( , )P P P x y  
 
 
 
2 2
1 2
2 2
1
2 2
2 2
2 2
2
2 2
2 2
, (0 0) (4 0)
16 4
, ( 0) ( 0)
4
16
, ( 0) ( 4)
( 4) 4
( 4) 16
d P P
d P P x y
x y
x y
d P P x y
x y
x y
   
 
   
  
  
   
   
   
Therefore,
 22
2 2
4
8 16
8 16
2
y y
y y y
y
y
 
  


which gives
2 2
2
2 16
12
2 3
x
x
x
 

 
Two triangles are possible. The third vertex is
   2 3, 2 or 2 3, 2 .
59. 2 2
1 2
2 2
( , ) ( 4 2) (1 1)
( 6) 0
36
6
d P P     
  


 2 2
2 3
2 2
( , ) 4 ( 4) ( 3 1)
0 ( 4)
16
4
d P P       
  


2 2
1 3
2 2
( , ) ( 4 2) ( 3

Loading page 15...

Chapter 1: Graphs
10
62.    2 2
1 2
2 2
( , ) 4 7 0 2
( 11) ( 2)
121 4 125
5 5
d P P     
   
  

 2 2
2 3
2 2
( , ) 4 ( 4) (6 0)
8 6 64 36
100
10
d P P     
   


   2 2
1 3
2 2
( , ) 4 7 6 2
( 3) 4 9 16
25
5
d P P    
    


Since      2 2 2
1 3 2 3 1 2( , ) ( , ) ( , )d P P d P P d P P  ,
the triangle is a right triangle.
63. Using the Pythagorean Theorem:
2 2 2
2
2
90 90
8100 8100
16200
16200 90 2 127.28 feet
d
d
d
d
 
 

  
90
9090
90
d
64. Using the Pythagorean Theorem:
2 2 2
2 2
60 60
3600 3600 7200
7200 60 2 84.85 feet
d
d d
d
 
   
  
60
6060
60
d
65. a. First: (90, 0), Second: (90, 90),
Third: (0, 90)
(0,0)
(0,90)
(90,0)
(90,90)
X
Y
b. Using the distance formula:
2 2
2 2
(310 90) (15 90)
220 ( 75) 54025
5 2161 232.43 feet
d    
   
 
c. Using the distance formula:
2 2
2 2
(300 0) (300 90)
300 210 134100
30 149 366.20 feet
d    
  
 
66. a. First: (60, 0), Second: (60, 60)
Third: (0, 60)
(0,0)
(0,60)
(60,0)
(60,60)
x
y
b. Using the distance formula:
2 2
2 2
(180 60) (20 60)
120 ( 40) 16000
40 10 126.49 feet
d    
   
 
c. Using the distance formula:
2 2
2 2
(220 0) (220 60)
220 160 74000
20 185 272.03 feet
d    
  
 

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Solution Manual for Precalculus, 11th Edition

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